Consider trying to use Solomonoff induction to reason about P(I see “Canada goes to war with USA” in next year), emphasis added:
In Solomonoff induction, since we have unlimited computing power, we express our uncertainty about a 1920×1080 video frame the same way. All the various pixel fields you could see if your eye jumped to a plausible place, saw a plausible number of dust specks, and saw the box flash something that visually encoded ’14′, would have high probability. Pixel fields where the box vanished and was replaced with a glow-in-the-dark unicorn would have very low, though not zero, probability.
ASHLEY: Can we really get away with viewing things that way?
BLAINE: If we could not make identifications like these in principle, there would be no principled way in which we could say that you had ever expected to see something happen—no way to say that one visual field your eyes saw had higher probability than any other sensory experience. We couldn’t justify science; we couldn’t say that, having performed Galileo’s experiment by rolling an inclined cylinder down a plane, Galileo’s theory was thereby to some degree supported by having assigned a high relative probability to the only actual observations our eyes ever report.
ASHLEY:I feel a little unsure of that jump, but I suppose I can go along with that for now. Then the question of “What probability does Solomonoff induction assign to Canada invading?” is to be identified, in principle, with the question “Given my past life experiences and all the visual information that’s entered my eyes, what is the relative probability of seeing visual information that encodes Google News with the headline ‘CANADA INVADES USA’ at some point during the next 300 million seconds?”
I think that ~”binary classification of all possible pixel combinations is the only way you can demonstrated constrained anticipations” claim is wrong, and don’t know why the heck it’s stated so strongly. [EDIT: possibly because Blaine is saying it, who’s supposed to be a huge Solomonoff Induction fan?] Here’s a possible counterexample, which I think could end up leading to another principled answer:
I have some predictive neural circuits which, as a matter of mechanistic neuroscience, predict the imminent firing of other neural circuits which (as another matter of fact) are edge detectors → letter detectors → “Google news” detectors; similar stories for internal war neurons, Canada neurons, etc.
The predictive circuits are predicting (by means of action potentials and other neural information) that the other neural circuits and concepts will fire soon.
(1) and (2) ⇒ I expect to see the visual news of war with Canada. This does not imply a probability distribution over all possible “pixel configurations” (itself an inappropriate way of describing retinal activations). And yet it still describes constrained anticipations.
This description isn’t mathematical, but in other ways it’s more satisfactory than Solomonoff. It gestures at something which actually happens in reality, and it doesn’t require infinite computation.
But when an idealization is really appropriate, arguments for it shouldn’t feel like a “jump.” They just feel right.
Anyways, being able to classify all pixel-combinations seems absurd, even in principle. While there exist mathematical functions from pixel-space to {0,1} which just accept “obvious accepts”… There are so many pixel configurations, and tons of them implicitly exploit any reasonably simple classifier you can dream up. This basically seems like an extension of the problem that you can’t get an adversarially robust classifier over sense data. Possible in principle, perhaps, but probably not in a way which leaves out degrees of freedom in deciding which ambiguous cases “count” as war-indicating-pixels.
I’m lightly updating that Solomonoff-inspired reasoning is more likely to be misleading / bogus / irrelevant / ill-founded. (EDIT: But I still overall think SI contains useful insights.)
Point made/inspired by a recent Jonathan Stray talk.
Consider trying to use Solomonoff induction to reason about P(I see “Canada goes to war with USA” in next year), emphasis added:
I think that ~”binary classification of all possible pixel combinations is the only way you can demonstrated constrained anticipations” claim is wrong, and don’t know why the heck it’s stated so strongly. [EDIT: possibly because Blaine is saying it, who’s supposed to be a huge Solomonoff Induction fan?] Here’s a possible counterexample, which I think could end up leading to another principled answer:
I have some predictive neural circuits which, as a matter of mechanistic neuroscience, predict the imminent firing of other neural circuits which (as another matter of fact) are edge detectors → letter detectors → “Google news” detectors; similar stories for internal war neurons, Canada neurons, etc.
The predictive circuits are predicting (by means of action potentials and other neural information) that the other neural circuits and concepts will fire soon.
(1) and (2) ⇒ I expect to see the visual news of war with Canada. This does not imply a probability distribution over all possible “pixel configurations” (itself an inappropriate way of describing retinal activations). And yet it still describes constrained anticipations.
This description isn’t mathematical, but in other ways it’s more satisfactory than Solomonoff. It gestures at something which actually happens in reality, and it doesn’t require infinite computation.
But when an idealization is really appropriate, arguments for it shouldn’t feel like a “jump.” They just feel right.
Anyways, being able to classify all pixel-combinations seems absurd, even in principle. While there exist mathematical functions from pixel-space to {0,1} which just accept “obvious accepts”… There are so many pixel configurations, and tons of them implicitly exploit any reasonably simple classifier you can dream up. This basically seems like an extension of the problem that you can’t get an adversarially robust classifier over sense data. Possible in principle, perhaps, but probably not in a way which leaves out degrees of freedom in deciding which ambiguous cases “count” as war-indicating-pixels.
I’m lightly updating that Solomonoff-inspired reasoning is more likely to be misleading / bogus / irrelevant / ill-founded. (EDIT: But I still overall think SI contains useful insights.)
Point made/inspired by a recent Jonathan Stray talk.